Finite volume methods apply directly to the conservation law form of a differential equation
system; and they commonly yield cell average approximations to the unknowns rather than …

This paper reports on the results of a three-year research effort aimed at investigating and
exploiting the role of physically motivated asymptotic analysis in the design of numerical …

The correction procedure via reconstruction (CPR, formerly known as flux reconstruction) is
a framework of high order methods for conservation laws, unifying some discontinuous …

We develop essentially non-oscillatory (ENO) finite volume methods on conforming triangulations
for the numerical solution of hyperbolic conservation laws. Besides theoretical results …

During the last three decades geosciences and geo-engineering were influenced by two
essential scenarios: First, the technological progress has changed completely the …

This book provides a thrilling history of the famous priority dispute between Gottfried Wilhelm
Leibniz and Isaac Newton, presenting the episode for the first time in the context of cultural …

The theory of optimal recovery is applied to finite volume methods for the numerical solution
of conservation laws in multiple space dimensions. Classical polynomial EN0 (essentially …

The flux reconstruction is a framework of high order semidiscretisations used for the numerical
solution of hyperbolic conservation laws. Using a reformulation of these schemes relying …

… Finally, I wish to thank several colleagues for suggestions, particularly Thomas Sonar, who
contributed to Chapter 7 when we organized a joint course for graduate students,1) and Dr. …

Radial basis functions are used in the recovery step of finite volume methods for the
numerical solution of conservation laws. Being conditionally positive definite such functions …